然而，这种无风险借贷的假设是不现实的。布莱克(1972)开发了一个CAPM模型，他没有做出这种极端的假设。他指出，通过允许卖空风险资产，可以获得平均方差有效投资组合。黑色和sharpel - lintner模型的不同之处在于。Black观察到，这必须低于预期的市场回报，这使得市场beta的溢价是积极的。在Sharpe-Lintner模型中，预期回报是无风险利率。关于卖空行为的黑色假设也不现实。因为，如果没有风险资产(sharpe- lintner版本)，如果有不受限制的卖空风险资产(黑色版本)，那么有效的投资组合实际上是不高效的，而且市场beta和CAPM(Fama和French:2003)之间没有任何关系。CAPM模型建立在一些极端假设上。为了证明这些模型的有效性，研究人员对市场数据进行了模型测试。本文将对一些实证研究进行研究。
However, this assumption of riskless borrowing and lending is unrealistic. Black (1972) developed a CAPM model where he did not make this extreme assumption. He showed that the mean variance efficient portfolio can be obtained by allowing the short selling of the risky assets. The Black and Sharpe-Lintner model differ in terms of the . Black observed that has to be less than the expected market return which allows the premium for the market beta to be positive. In the Sharpe-Lintner model the expect return was the risk free interest rate. The assumption that Black made about short selling is not realistic either. Because, if there is no risky asset (Sharpe-Lintner version) and if there is unrestricted short selling of the risky asset (Black version) then the efficient portfolio is actually not efficient and there does not exist any relation between market beta and CAPM (Fama and French: 2003). So, the CAPM models are built on some extreme assumptions. To testify the validity of these models researchers have tested the model against the market data. In this paper we will investigate some of those empirical researches.